To send an SMS from a new Twilio number using the C Shell, first set up your Twilio credentials by logging into your account and copying the `account_sid` and `auth_token`. Then, use the `curl` command to query Twilio's REST API for available phone numbers, purchase one, and store its value in a variable. Next, modify the `your_number` variable with your verified Twilio number and send an SMS using another `curl` command, specifying the required parameters such as `Body`, `From`, and `To`. This process allows you to automate sending SMS messages without leaving the C Shell, streamlining prototyping and development time.